Evaluation of Holomorphic Ackermanns

Dmitrii Kouznetsov

doi:doi:10.11648/j.acm.20140306.14

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Evaluation of Holomorphic Ackermanns

Dmitrii Kouznetsov

Published in Applied and Computational Mathematics (Volume 3, Issue 6)

Received: 21 November 2014 Accepted: 17 December 2014 Published: 27 December 2014

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Abstract

Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.

Published in	Applied and Computational Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.acm.20140306.14
Page(s)	307-314
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Ackermann Function, Superfunction, Tetration, Pentationx

References

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[7]	https://bbuseruploads.s3.amazonaws.com/bo198214/bunch/downloads/main.pdf Henryk Trappmann, Dmitrii Kouznetsov. 5+ methods for real analytic tetration. June 28, 2010.
[8]	http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html https://www.researchgate.net/publication/220576905_Portrait_of_the_four_regular_super-exponentials_to_base_sqrt%282%29 http://eretrandre.org/rb/files/Kouznetsov2009_215.pdf http://www.ils.uec.ac.jp/~dima/PAPERS/2010q2.pdf http://mizugadro.mydns.jp/PAPERS/2010q2.pdf D.Kouznetsov, H.Trappmann. Portrait of the four regular superexponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
[9]	http://link.springer.com/article/10.3103%2FS0027134910010029 https://www.researchgate.net/publication/226675861_Superfunctions_and_sqrt_of_factorial D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian version: p.8-14)
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APA Style

Dmitrii Kouznetsov. (2014). Evaluation of Holomorphic Ackermanns. Applied and Computational Mathematics, 3(6), 307-314. https://doi.org/10.11648/j.acm.20140306.14

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ACS Style

Dmitrii Kouznetsov. Evaluation of Holomorphic Ackermanns. Appl. Comput. Math. 2014, 3(6), 307-314. doi: 10.11648/j.acm.20140306.14

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AMA Style

Dmitrii Kouznetsov. Evaluation of Holomorphic Ackermanns. Appl Comput Math. 2014;3(6):307-314. doi: 10.11648/j.acm.20140306.14

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@article{10.11648/j.acm.20140306.14,
  author = {Dmitrii Kouznetsov},
  title = {Evaluation of Holomorphic Ackermanns},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {307-314},
  doi = {10.11648/j.acm.20140306.14},
  url = {https://doi.org/10.11648/j.acm.20140306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.14},
  abstract = {Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.},
 year = {2014}
}

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T1  - Evaluation of Holomorphic Ackermanns
AU  - Dmitrii Kouznetsov
Y1  - 2014/12/27
PY  - 2014
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Author Information

Dmitrii Kouznetsov

Institute for Laser Science, University of Electro-Communications, 1-5-1 Chofugaoka, Chofushi, Tokyo, 182-8585, Japan

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APA Style

Dmitrii Kouznetsov. (2014). Evaluation of Holomorphic Ackermanns. Applied and Computational Mathematics, 3(6), 307-314. https://doi.org/10.11648/j.acm.20140306.14

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ACS Style

Dmitrii Kouznetsov. Evaluation of Holomorphic Ackermanns. Appl. Comput. Math. 2014, 3(6), 307-314. doi: 10.11648/j.acm.20140306.14

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AMA Style

Dmitrii Kouznetsov. Evaluation of Holomorphic Ackermanns. Appl Comput Math. 2014;3(6):307-314. doi: 10.11648/j.acm.20140306.14

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@article{10.11648/j.acm.20140306.14,
  author = {Dmitrii Kouznetsov},
  title = {Evaluation of Holomorphic Ackermanns},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {6},
  pages = {307-314},
  doi = {10.11648/j.acm.20140306.14},
  url = {https://doi.org/10.11648/j.acm.20140306.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.14},
  abstract = {Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Evaluation of Holomorphic Ackermanns
AU  - Dmitrii Kouznetsov
Y1  - 2014/12/27
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140306.14
DO  - 10.11648/j.acm.20140306.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 307
EP  - 314
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.14
AB  - Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.
VL  - 3
IS  - 6
ER  -

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